Fuzzy logics based on [0,1)-continuous uninorms

D Gabbay, G Metcalfe

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)

Abstract

Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hajek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics
Original languageEnglish
Pages (from-to)425 - 449
Number of pages25
JournalARCHIVE FOR MATHEMATICAL LOGIC
Volume46
Issue number5-6
DOIs
Publication statusPublished - Jul 2007

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